A new distributed positioning algorithm was proposed for unknown nodes in a three-dimensional wireless sensor network.First,assuming that there are some anchor nodes in WSN,the positions of which are already known,geometric relationships and communication constraints among the unknown nodes and the anchor nodes were founded based on the assistant three-dimensional coordinates system.Then the constructing method of a curving three-dimensional graph containing an unknown node was researched based on the geometric relationships and communication constraints.The curving three-dimensional graph was constructed by calculating several profiles and curving planes.It was converted to a plane three-dimensional graph,which is composed of several profiles,to diminish the communication and computational load of WSN.Sequentially,the centroid of the curving three-dimensional graph was obtained by calculation the centroid of plane three-dimensional graph.Finally,the centroid of curving three-dimensional graph was taken to be the estimated position of the unknown node.The algorithm fetches up the blank of algorithms which are used to position the unknown nodes in a three-dimensional WSN.It is range-free,distributed and based exclusively on connectivity.Since the algorithm is very simple and the only communication needed is between the anchor nodes and the unknown node,the communication and computational loads are very small.A theoretical analysis and simulation results show that it suitable for all sizes of low-power wireless sensor networks.